Temporal Drift
Integrating a white noise signal over time results in an output that wanders away from the origin. Random walk noise appears in the output of inertial sensors as an accumulation of small, unpredictable errors. It causes the position or orientation estimate to diverge from the true value.
Integral Relation
Rate sensors like gyroscopes exhibit this behavior when their angular rate signal is integrated to find the angle. The random walk noise magnitude grows with the square root of the elapsed time. This growth makes the error particularly problematic for long duration navigation tasks.
Data Averaging
Simple mean calculations do not reduce the variance of this type of fluctuation because the samples are not independent. An Allan variance plot is the standard tool for identifying random walk noise in high precision clocks and sensors. The slope of the plot at specific integration times reveals the presence of the random walk component.
Slope Identification
Identifying the noise type allows the designer to apply a Kalman filter with the correct error model. Proper modeling can mitigate the drift by combining the sensor data with other reference sources. Random walk noise sets the fundamental limit for dead reckoning accuracy.
